Question

find the square root of 784 using factorisation​

Answer 1

2 |784

2 |392

2 |196

2 |98

7 |49

7 |7

1

Thus, 784 can be factorized as follows ,

784 = 2 × 2 × 2 × 2 × 7 × 7

$= {2}^{2} \times {2}^{2} \times {7}^{2}$

Applying square root on both sides, we get,

$\sqrt{784} = \sqrt{ {2}^{2} \times {2}^{2} \times {7}^{2} } \\ = 2 \times 2 \times 7 \\ = 28$

Thus, by prime factorisation method, we obtain the square root of 784 to be 28.

The correct answer is 28.